
EXAMPLE: 7745 + 3289 = 11034 7+7+4+5 = 23 2+3 = 5 3+2+8+9 = 22 2+2 = 4 9 1+1+0+3+4 = 9 
To check subtraction is correct:
 add together the total and the number you subtracted and this should
equal the number you started with.
EXAMPLE: 4320 – 1978 = 2342 1978+2342 = 4320 
To check multiplication is
correct:
 divide the answer by one of the numbers being
multiplied.
EXAMPLE: 27 x 19 = 513 513 Ã· 19 = 27 
To check division is
correct:
 multiply the answer by the number you originally
divided by and this answer should be the same as the original number being divided.
EXAMPLE: 798 Ã· 14 = 57 57 x 14 = 798 
HANDY HINTS
If two columns of figures should balance but don’t, subtract one
total from the other and if the difference is 1, 10, 100, 9 or 99 you have probably made
an error in addition.
If the difference is divisible by 9 you have probably transposed a
figure (e.g. written 89 instead of 98).
This was also sent in by KB who gave the following
illustration –
If your balance says 45.25 but your
statement says 42.55 – the difference is 2.70 which is
divisible by 9 so, therefore, it is probably a transposed figure. You can see the 5
and 2 have been transposed.
To “square” a number (i.e. multiply a number by
itself e.g. 17 x 17)
Example A – 17 x 17
First partition the number – 10, 7  
Square the 10 (i.e. 10 x 10)  = 100 
Square the 7 (i.e. 7 x 7)  = 49 
Then 2 x (10 x 7)  = 140 
 = 289 
Example B – 52 x 52
Partition the number – 50, 2  
Square the 50 (50 x 50)  = 2,500 
(5 x 5 plus two noughts)  
Square the 2 ( 2 x 2)  = 4 
Then 2 x (50 x 2)  = 200 
52 x 52  = 2,704 
This shortcut was sent in by
Sue Knight – thanks.
An easy way to remember your nine times table is –
a: The figures in the answer always total 9
e.g.
2 x 9 = 18 (1+8 =
9):
7 x 9 = 63 (6+3 = 9)
b: Deduct 1 from the number you are multiplying and the second
number in the answer then becomes obvious (as it must
total 9).
To multiply 8 x 9
Deduct 1 from the 8 = 7 (this is the first number of the
answer)
The numbers in the answer always total 9 so the second number
must be 2
Therefore 8 x 9 =72
Now for the 11 times table –
a: Add together the digits you are multiplying e.g. 33 x 11 add the 3 + 3 =6
b: Place the the answer in between the two digits e.g.
363
Therefore 33 x 11 = 363
If the two digits add up to more than
ten (e.g. 48 x 11 where 4+8=12) then you have to
add the 1 to the 4 and place the 2 in the middle of the two numbers.
Therefore 48 x 11 = 528
If you ever need to find out the sum of all the numbers
between two given digits, here is the formula :
ADD TOGETHER THE FIRST NUMBER AND THE LAST NUMBER IN THE SEQUENCE
THEN MULTIPLY BY THE NUMBER OF THE MIDDLE NUMBER IN THE SEQUENCE.
I will try to explain – say you wanted to find out the total of
numbers 7 through to 35.
i.e. 7+8+9 +10+11 an so on until..33+34+35.
First add the first number in the
sequence to the last number in the sequence, which in this case is – 7 + 35 = 42
Then to find the NUMBER of the middle digit in the sequence you
deduct the lowest number from the highest number, add 1 then divide by 2
i.e. 35 – 7 = 28 + 1 = 29
divided by 2 =14.5
NOW MULTIPLY 42 X 14.5 = 609
SO THE SUM OF ALL FIGURES BETWEEN 7
AND 35 = 609
Now all you accountants out there – give us some more (or have you
forgotten them!) – contact us on june@hintsandthings.co.uk.
For more mathematical shortcuts
click here.